SIAM AG on Orthogonal Polynomials and Special Functions


Extract from OP-SF NET

From: Vadim I. Zelenkov ( and Vadim A. Savva (
Subject: VI International Krawtchouk Conference: Kiev, Ukraine, May 14-17, 1997

The number of classical orthogonal polynomials systems of a discrete variable is highly restricted, hence each discoverer of such an OPS deserves to be known to the scientific community not only as a mathematician but also as an individual. That's why it is very strange to find only some morsels of information about the author of Sur une généralisation des polynômes d'Hermite published in 1929 which initiated a new stage in the theory of orthogonal polynomials.

The reason is both simple and tragic.

Mykhailo Pilipovich (in Ukrainian; in Russian his name is sounded Mikhail Philippovich) Krawtchouk was born on September 27, 1892 in the small village of Chovnitsy (Western Ukraine). After graduating from gymnasium he entered Kiev St. Vladimir University, obtaining his first diploma degree in 1914---on the eve of the First World War. Thus the young mathematician had to move to Moscow because of the University evacuation. On September 5, 1917 (80 years ago) he gave his first lecture.

After the 1917 revolution, M. Krawtchouk worked in various Kiev universities, institutes, gymnasia, then for two years of the civil war (1919-1921) he was the head of a rural school near Kiev.

When the situation in the then USSR became relatively stabilized, Krawtchouk got the opportunity for fruitful scientific work. The title of his doctoral thesis was On Quadratic Forms and Linear Transform (1924). He took part in the International Mathematical Congresses in Toronto (1924) and Bologna (1928), had close contacts with Hadamard, Hilbert, Courant, Tricomi, i.a. In 1929 he became a full member of the All-Ukrainian Academy of Sciences.

The list of M. Krawtchouk's scientific works contains about 180 titles including such branches of mathematics as the theory of permutation matrices, theory of algebraic, transcendental, differential and integral equations, introduction and use of polynomials associated with the binomial distribution (Krawtchouk polynomials), etc. Moreover his efforts were applied in the fields of philosophy, history of mathematics and mathematical education. It is especially important for the independent Ukraine that it was M. Krawtchouk who was in charge of editing the first three-volume dictionary of Ukrainian mathematical terminology. (Having a knowledge of French, German, Italian, Polish and, of course, Russian, he delivered lectures and wrote articles mostly in Ukrainian).

Anyone knowing even a little Soviet history of the thirties can conclude that Krawtchouk could not avoid the Great Terror. During the Orwellian "hours of hatred" in 1937 he was being denounced as a "Polish spy", "bourgeois nationalist" etc. In 1938, he was arrested and sentenced to 20 years of confinement and 5 years of exile.

Academician Krawtchouk, the author of the results which became part of the world's mathematical knowledge, the brilliant lecturer who inspired many outstanding followers (e.g., Sergey Korolev, the future leader of the Soviet space programme), the member of the French, German and other Mathematical Societies died on March 9, 1942 in Kolyma branch of GULAG (North-Eastern Siberia) more than 6 months short of his 50th birthday.

M. Krawtchouk was officially rehabilitated in 1956 and restored as a member of the Academy of Sciences only in March 1992, 50 years after his death.

Tempora mutantur, the times are changing, and in September 1992 the First International M. Krawtchouk Conference was held in the Ukraine. Since then such conferences have been yearly.

The 6th International Scientific Krawtchouk Conference took place in Kiev from May 15th to 17th 1997. The organizers were the Ukrainian Ministry of Education, Institute of Mathematics, National Academy of Sciences of Ukraine and National Technical University of Ukraine (formerly Kiev Polytechnical Institute where M. Krawtchouk in his time was the head of the Mathematical Chair).

The opening ceremony included speeches from members of the Organizing Committee, addresses from M. Krawtchouk's relatives and followers and some splendid Ukrainian songs executed by a chorus.

The scientific agenda consisted of about 380 reports divided into four sections according to Krawtchouk's scientific interests: Differential and Integral Equations, their Application; Algebra, Geometry, Mathematical and Numerical Analysis; Probability Theory and Mathematical Statistics; History and Teaching Methods of Mathematics. Most of the participants represented the Ukraine, 19 reports were from Russia, 4 from Belarus and 1 from the Czech Republic. Many participants were postgraduates and young scientists presenting their first results.

Let us mention some of the titles which could be of interest to the readers of the Newsletter:

Most of the conference materials have been published in Ukrainian; some of them are in Russian and some in English.

An additional circumstance which made the conference especially attractive was the pleasant weather and the famous Kiev chestnut trees blooming on schedule in May. We were impressed by ancient Kiev though we had visited it repeatedly before (Belarus is not so far from the Ukraine!).

The participants are grateful to the Organizing Committee led by Academician M. Zgurovskyi and especially to Professor Nina Virchenko who carried out enormous work. Moreover, for about thirty years she has studied the biography of M. Krawtchouk and the authors of this report would like to express their personal thanks for the permission to use some of her articles while preparing this text.

The details of the 7th Krawtchouk Conference (1998) are now under discussion. You can send your inquiries to the address:

Professor Nina Virchenko
Dept. of Mathematics No. 1
National Technical University of Ukraine (KPI)
37, Peremogi Avenue
252056, Kiev, Ukraine.

Vadim I. Zelenkov
Vadim A. Savva

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